Temperature dependence of plasmonic terahertz absorption ... - Physics

APPLIED PHYSICS LETTERS 96, 042105 共2010兲

Temperature dependence of plasmonic terahertz absorption in grating-gate gallium-nitride transistor structures A. V. Muravjov,1,2,a兲 D. B. Veksler,1 V. V. Popov,3 O. V. Polischuk,3 N. Pala,4 X. Hu,5 R. Gaska,5 H. Saxena,6 R. E. Peale,6 and M. S. Shur1 1

Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA 2 Institute for Physics of Microstructures, RAS, Nizhny, Novgorod 603950, Russia 3 Kotelnikov Institute of Radio Engineering and Electronics, RAS, Saratov 410019, Russia 4 Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA 5 Sensor Electronic Technology, Inc., 1195 Atlas Road, Columbia, South Carolina 29209, USA 6 Department of Physics, University of Central Florida, Orlando, Florida 32816, USA

共Received 12 July 2009; accepted 21 December 2009; published online 26 January 2010兲 Strong plasmon resonances have been observed in the terahertz transmission spectra 共1–5 THz兲 of large-area slit-grating-gate AlGaN/GaN-based high-electron-mobility transistor 共HEMT兲 structures at temperatures from 10 to 170 K. The resonance frequencies correspond to the excitation of plasmons with wave vectors equal to the reciprocal lattice vectors of the metal grating, which serves both as a gate electrode for the HEMT and a coupler between plasmons and incident terahertz radiation. Wide tunability of the resonances by the applied gate voltage demonstrates potential of these devices for terahertz applications. © 2010 American Institute of Physics. 关doi:10.1063/1.3292019兴 Plasma excitations 共plasmons兲 in field-effect transistors with two-dimensional 共2D兲 electron channels strongly affect terahertz 共THz兲 properties of these devices.1 Faster plasmon velocities in comparison with electron drift velocities enable plasmonic devices to break into the THz range of operation frequencies.1–11 Critical issues for future development of the plasmon electronics are ensuring a strong coupling between plasmons and THz radiation and feasibility of room temperature operation. Previously, pronounced 2D plasmons in Si,2,3 III-V compound,5–12 and GaN13 based semiconductor structures were observed only below liquid nitrogen temperatures. In this letter, we present our results on the observation of plasmon resonances in large-area slit-grating-gate AlGaN/ GaN-based high-electron-mobility transistor 共HEMT兲 structures 共Fig. 1兲 at temperatures up to 170 K in agreement with theoretical predictions of Ref. 14. The AlGaN/GaN heterostructure was grown on sapphire substrate by migration enhanced metal-organic chemical vapor deposition 共MEMOCVD®兲 technique. The heterostructure consisted of a 100 nm thick AlN buffer layer, 1.4 ␮m thick undoped GaN layer, followed by Al0.2Ga0.8N barrier layer, Si-doped to approximately 2 ⫻ 1018 cm−3. A metal grating gate with the period L = 1.5 ␮m was deposited on top of the structure. Individual gate-finger length was W = 1.15 ␮m with 0.35 ␮m slits between adjacent fingers. The thickness of the AlGaN barrier layer was d = 28⫾ 2 nm. Contacts for the source/drain and gate electrodes were fabricated using e-beam evaporated Ti/Al/Ti/Au and Ni/Au metal stacks, respectively. The metal grating served both as a gate electrode and a coupler between plasmons and incident THz radiation. The 2D electron concentration N1 in the channel under the grating-gate fingers was controlled by the gate voltage Ug referenced to the connected source and drain electrodes. The electron sheet density in the channel under grating-gate fina兲

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gers can be estimated as N1 = ␧␧0共Ug − Uth兲 / ed, where Uth is the channel depletion threshold voltage, ␧ is the dielectric constant of the barrier layer, ␧0 is the free-space permittivity, and e is the electron charge. The threshold voltage estimated from the transconductance measurements is Uth ⬇ −4 V, which yields N1 ⬇ 7.5⫻ 1012 cm−2 for Ug = 0 at room temperature. Large active area of the device 共1.6⫻ 1.7 mm2 with more than 1000 metal fingers兲 allowed efficient focusing of incident THz radiation and its study by methods of conventional Fourier transform infrared 共FTIR兲 spectroscopy. Transmission spectra of the structure were measured by Bruker IFS 66 v/S FTIR spectrometer at liquid nitrogen temperatures and above,15,16 and by Bomem DA8 Fourier spectrometer below liquid nitrogen temperature 共see Ref. 12 for details兲. In both experiments, the original spectral resolution was 0.03 THz, which was sufficient for resolving the Fabry– Perot fringes 共⌬␯ = 0.1 THz兲 caused by multiple reflections between the structure and the back of the sapphire substrate. To eliminate these interference effects, the spectra were averaged over the period of the Fabry–Perot oscillations, which reduced the effective resolution to 0.1 THz. The transmission

FIG. 1. Grating-gate HEMT structure 共left兲. THz radiation with polarization of the electric field across the gate fingers is incident from the top; scanning electron microscopy image of the grating-gate fragment with L = 1.5 ␮m, W = 1.15 ␮m 共right兲.

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FIG. 2. 共Color online兲共a兲 Transmission spectra of the grating-gate AlGaN/ GaN HEMT structure, referenced to free space, measured at temperatures from 77 K to 295 K for Ug = 0. Resolution is 0.1 THz. 共b兲 Transmission spectra for different applied gate voltages Ug,appl = 共0 V ; −1 V ; −2 V ; −3 V ; −4 V ; and − 5 V兲 at T = 10 K. Resolution is 0.1 THz. The spectra are referenced to the transmission spectrum of the identical AlGaN/GaN device without metal gate grating.

spectra measured at temperatures 77, 120, and 170 K exhibit well pronounced resonances at the fundamental plasma frequency and its second, third, and fourth harmonics 关Fig. 2共a兲兴. Observed resonance frequencies are in a good agreement with plasmon dispersion law ␻p = skp and selection rule for the plasmon wave vector as kp = 2␲n / L 共n = 1 , 2 , 3 , 4. . .兲,17 where the plasmon velocity is s = 共e2N1d / mⴱ␧␧0兲1/2 with mⴱ being the electron effective mass. For N1 = 7.5⫻ 1012 cm−2, one obtains s ⬇ 1.9 ⫻ 108 cm/ s. The resonances obey this simple dispersion law for gated plasmons due to relatively large grating-gate duty cycle W / L ⬇ 0.77 and small gate-to-channel separation d Ⰶ L. However, because of alternating gated and ungated regions, the actual value of s is also a weak function of the ratio W / L and of the resonance order n, which results in slightly nonequidistant behavior of the resonances exhibited in Fig. 2共a兲. Figure 2共b兲 demonstrates tunability of the resonances by the applied gate voltage Ug. Negative Ug decreases the electron concentration N1 under the gate fingers, decreasing plasmon velocity s and, hence, causing redshift of the resonances. The best fit of the resonance shift versus Ug for the first, second, and third resonances in Fig. 2共b兲 corresponds to Uⴱth ⬇ −8 V, while the value of Uth found from the transconductance measurements is about ⫺4 V. We explain this by a voltage drop across the channel caused by the gate leakage current crowding at the edges of the structure. The gate leakage conductivity is about 0.005 ⍀−1 at T = 10 K, while the conductivity of the channel is about 0.02 ⍀−1 共for Ug = 0兲. As a result, the applied gate voltage Ug,appl 关specified in Fig. 2共b兲兴 appears almost two times higher than the actual

FIG. 3. 共Color online兲共a兲 Calculated transmission 共T兲 spectra of the gratinggate AlGaN/GaN HEMT structure for different electron mobilities: 共1兲 ␮77 K = 10 000 cm2 / V s 共␶ = 1.14⫻ 10−12 sec兲, 共2兲 ␮120 K = 7600 cm2 / V s 共␶ = 0.86⫻ 10−12 sec兲, 共3兲 ␮170 K = 4400 cm2 / V s 共␶ = 0.5⫻ 10−12 sec兲, and 共4兲 ␮295 K = 1200 cm2 / V s 共␶ = 0.14⫻ 10−12 sec兲. 共b兲 Corresponding calculated absorption 共A兲 and reflection 共R兲 spectra.

voltage Ug between the gates and the channel in the central part of the structure. Numerical simulations of the THz plasmon transmission spectra were performed using the approach developed in Ref. 18. The response of 2D electrons to incident THz radiation was described by the sheet conductivity using the local Drude model as

␴共␻兲 =

e2N1,2␶ , mⴱ共1 − i␻␶兲

where N1 and N2 are the steady-state electron densities in the gated and ungated parts of the channel, respectively 共see Fig. 1兲, and ␶ is a phenomenological electron scattering time related to the electron mobility, ␮, as ␶ = ␮mⴱ / e. Parameters of the structure used in the numerical simulations were mⴱ = 0.2m0 with m0 being the free-electron mass, ␧ = 9.5, d = 28 nm, N1 = N2 = 7.5⫻ 1012 cm−2. Gold fingers of the grating gate were considered as 2D strips with the sheet conductivity equal to 2.5 S. However the assumption of perfectly conductive strips yielded no significant difference in the results. The electron mobility ␮ was used as a fitting parameter in the simulations in order to achieve best correspondence between linewidths and intensities of the plasmon resonances in the calculated 共Fig. 3兲 and measured 关Fig. 2共a兲兴 transmission spectra for each temperature. These fitted values of ␮ 共see the caption of Fig. 3兲 are in good agreement with previously reported electron mobilities in AlGaN/GaN heterostructures at the same temperatures.19 Due to relatively high electron concentration in AlGaN/ GaN heterojunction, the criterion for resolving adjacent reso-


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nance lines 共␻p␶p Ⰷ 1兲 is satisfied up to 170 K. Plasmon relaxation time ␶p in our numerical simulations was defined by the electron scattering rate and plasmon radiative decay.20 Accurate comparison between the experimental and calculated linewidths of the resonances allowed us to evaluate the role of electron fluid viscosity ␯, as another plasmon damping mechanism4 potentially affecting ␶p. Viscosity contribution to the resonance linewidth is 2␯k2p, and, hence, should be especially pronounced for plasmon modes with larger wave vectors.4 Slight broadening of the higher-order resonances in the measured spectra beyond the numerically simulated linewidths allowed us to estimate the upper bound for the electron viscosity as 10 cm2 / s. In conclusion, the observed depth of the resonances is the result of strong coupling between incident THz radiation and plasmons 共high plasmon radiative decay rate兲,20 achieved by using a grating gate with relatively narrow slits.14 At elevated temperatures faster plasmon radiative decay, and thus narrower slits, are required to satisfy the conditions of optimal coupling, where the absorption of the radiation by plasmons reaches a maximum A = 0.5共1 − 冑R0兲共R0 ⬇ 0.25 is the reflectivity of sapphire兲, and the plasmon radiative decay rate is equal to 1/2 of the electron scattering rate.20 In our case, such conditions are achieved at the temperature 120 K 关Fig. 3共b兲兴. Below 120 K the radiative decay of plasmons becomes dominant causing efficient resonant reflection from the plasma layer with R reaching 65% at 77 K. The work at RPI was supported by the U.S. ONR. The work at SET has been partially supported by NASA STTR Phase I under Contract No. NNX09CF26P 共Program Monitor Dr. Nurul Abedin兲. The work at the Kotelnikov Institute was supported by the RFBR 共Grant Nos. 09-02-00395 and 08-02-92497兲 and by the Russian Academy of Sciences Program “Fundamentals of Nanotechnologies and Nanomaterials.” A.V.M. thanks RFBR for partial support of work at IPM RAS 共Grant No. 07-02-01487a兲. R.E.P. and H.S. thank Air Force Research Laboratory, Hanscom AFB MA for supporting the work at UCF 共Grant No. FA871807C0036兲.

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